Question: Solve for $x$ : $x^2 - 4x + 3 = 0$
The coefficient on the $x$ term is $-4$ and the constant term is $3$ , so we need to find two numbers that add up to $-4$ and multiply to $3$ The two numbers $-1$ and $-3$ satisfy both conditions: $ {-1} + {-3} = {-4} $ $ {-1} \times {-3} = {3} $ $(x {-1}) (x {-3}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x -1) (x -3) = 0$ $x - 1 = 0$ or $x - 3 = 0$ Thus, $x = 1$ and $x = 3$ are the solutions.